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Abstract

We present detailed results of analytical and numerical investigation of the Shockley surface states in photonic crystals doped with a chain of alternating s- and p-type defects. Conditions for the existence and control of such surface states are studied using the empirical tight-binding model and verified by the finite-difference time-domain technique. We show for the first time, to our knowledge, that, in contrast to the case of solids, the Shockley states in photonic crystals with complete unit cells of defects do not appear simultaneously with the opening of the inverted bandgap between s and p bands. Rather, the width of the inverted bandgap must reach a critical value equal to the separation between the discrete levels. This results in a system size effect of the Shockley states in photonic crystals. We show how such system size effect can be used to control the surface states. We also demonstrate the control of the Shockley states by controlling the overlap of s and p bands, achieved through change in either the radius of one of the defects or the refractive index via electro-optical effects.

References

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